as a novel generalization of the nonlinear Schrödinger (NLS) equation,
was first derived using bi-Hamiltonian structures of the NLS equation[1]},
where \(\nu \)  and \(\gamma \)  are real parameters.
This equation is integrable and belongs to
the derivative nonlinear Schrödinger (DNLS) hierarchy [2]}
that is related to the Kaup-Newell (KN) spectral problem.
It is notable that the FL equation (REF ) is equivalent to the following one [3]}
\(u_{xt}+u-2i\delta |u|^{2}u_{x}=0,~~\delta =\pm 1.\) 
